Significant Figures Calculator
Count the significant figures in a number, see which digits count, and round to any number of significant figures.
significant not significant ambiguous
Counting rules
Every non-zero digit counts, and so do zeros between them (the middle zero in 4050). Leading zeros only place the decimal point and do not count (0.004). Trailing zeros after a decimal point count (2.50 has three). Trailing zeros in a whole number without a decimal point are ambiguous, so measured values are best written in scientific notation.
Significant figures of values that trip people up
| Value | Significant figures |
|---|---|
0.004050 | 4 |
1200 | 2~4 (ambiguous) |
1200. | 4 |
3.20e5 | 3 |
100.0 | 4 |
0.0700 | 3 |
5.0 | 2 |
2.540 | 4 |
Worked example: how many digits to keep in a result
- Multiply or divide: keep the fewest significant figures. (2.5 V)/(0.0153 A) = 163.3987 Ω → 2.5 has two, so 160 Ω (write 1.6 × 10² Ω to make it clear)
- Add or subtract: keep the fewest decimal places. 12.11 + 0.3 + 1.003 = 13.413 → 0.3 has one decimal place, so 13.4
- Do not round in the middle of a calculation; round once at the end. Rounding at every step builds up error in the last digit.
Using it in practice
Step by step
- Type the number exactly as written on your data sheet, including trailing zeros and the decimal point.
- See which digits count as significant, highlighted in the result.
- Choose how many figures to keep and copy the rounded value.
Common mistakes
- Ambiguous trailing zeros. 1200 could have two, three or four significant figures. Write 1.20×10³ (or 1.20k) to say three.
- Rounding in the middle of a calculation. Keep extra digits until the final result, then round once. Rounding each step adds error.
- Applying the multiplication rule to addition. For products and quotients keep the smallest number of significant figures; for sums and differences keep the fewest decimal places.
How many figures to report
Your instrument decides. A 3½-digit multimeter showing 4.72 V gives three figures, and its accuracy spec may make the last one uncertain anyway. Reporting 4.71852 V from a calculator implies precision you did not measure. Exact numbers such as "2" in a full-wave formula or a count of readings do not limit significant figures.
Worked example: a time constant from bench values
You measured R = 4.68 kΩ on the meter (three significant figures) and the capacitor is marked 0.10 µF (two). The time constant is τ = RC = 4.68 kΩ × 0.10 µF = 0.468 ms. The capacitor limits the result to two figures, so you report τ = 0.47 ms.
If the next step is the cutoff frequency, keep the unrounded 0.468 ms: fc = (1)/(2πRC) = 340.07 Hz, reported as 3.4 × 10² Hz. Starting from the rounded 0.47 ms gives 338.6 Hz, which already moves the last digit you are allowed to keep. The 2 and the π are exact and never limit the figures.
Significant figures and meter uncertainty
Significant figures are a shorthand for uncertainty. When you know the real uncertainty, for example from a multimeter accuracy spec, let it decide the digits instead: round the uncertainty to one figure (two if it starts with 1), then round the value to the same decimal place. A reading of 4.62 kΩ with an uncertainty of 67 Ω becomes 4.62 ± 0.07 kΩ, and the calculator's 4.6823 kΩ from the same data would also be written 4.68 ± 0.07 kΩ.
Changing the unit prefix never changes the count: 0.0047 µF and 4.7 nF both have two significant figures. That is one more reason to use prefixes in a data table, because they remove leading zeros that readers must otherwise skip.
Frequently asked questions
How many significant figures does 0.004050 have?
Four: 4, 0, 5 and the final 0. The leading zeros only place the decimal point, while the zero between 4 and 5 and the trailing zero after the decimal point both count.
Does 1200 have two or four significant figures?
It is ambiguous. Without a decimal point the trailing zeros may just be placeholders, so it could be 2, 3 or 4. Write 1.2 × 10³, 1.20 × 10³ or 1.200 × 10³ to make it clear.